This contribution presents the probability distribution of the 'fixed' GPS baseline. This is the baseline which is used in fast and high precision GPS kinematic positioning. It follows from an ambiguity resolution process in which the carrier phase ambiguities are estimated as integers. For the estimation of the carrier phase ambiguities the principle of integer least-squares is used. By means of the 'fixed' baseline distribution it becomes possible to infer the quality of the positioning results. In particular their dependence on the quality of GPS ambiguity resolution is made clear. The mean and variance matrix of the 'fixed' baseline estimator are also determined. It shows that the 'fixed' baseline estimator is unbiased and that the difference of its precision with that of its conditional counterpart is governed by the precision of the integer least-squares ambiguities.

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